An electronic oscillator is an electronic circuit that produces a periodic (often a sine wave, a square wave, or a pulse trains) or a non-periodic (a double-mode wave or a chaotic wave) oscillating electronic signal. Oscillators convert direct current from a power supply to an alternating current signal, and are widely used in many electronic devices. This book surveys recent developments in the design, analysis and applications of this important class of circuits. Topics covered include an introduction to recent developments; analysis of bifurcation in oscillatory circuits; fractional-order oscillators; memristive and memcapacitive astable multivibrators; piecewise-constant oscillators and their applications; master-slave synchronization of hysteresis neural-type oscillators; multimode oscillations in coupled hard-oscillators; wave propagation of phase difference in coupled oscillator arrays; coupled oscillator networks with frustration; graph comparison and synchronization in complex networks; experimental studies on reconfigurable network of chaotic oscillators; fundamental operation and design of high-frequency tuned power oscillator; ring oscillators and selftimed rings in true random number generators; and attacking on-chip oscillators in cryptographic applications. Providing an overview of the state-of-the-art in oscillator circuits, this book is essential reading for researchers, advanced students and circuit designers working in circuit theory and modelling, especially nonlinear circuit engineering.

Oscillator circuit has been an absorbing theme of great interest for long time. The researchers of oscillator circuit have been working in order to develop various electrical engineering systems from radio communication circuits to clock generators for microprocessors. At the same time, synchronization of oscillator circuits has attracted attentions of many researchers not only in the electrical engineering field but also in the fields of mathematics, physics, chemistry, biology, medical science, neuroscience, social science, and so on. Oscillation waves (periodic or non-periodic) are the most basic and the most important signals in natural and artificial systems, and hence developing new oscillators and investigating synchronization and related phenomena in coupled oscillators are essential topics for many researchers in various fields. Oscillator circuits are good models of various systems generating oscillations in the sense that they are real physical systems realized easily and handled easily. This is the reason why oscillator circuits have been a common subject for researches in diverse fields.

In this chapter, we investigate the bifurcation phenomena observed in oscillatory circuits. The stability and bifurcation phenomena in autonomous systems are introduced by focusing on the equilibrium point and the fixed point. The characteristics and conditions of the saddle-node bifurcation, Hopf bifurcation, and pitchfork bifurcation are discussed for the equilibrium point. Likewise, the characteristics and conditions of the saddle-node bifurcation, period-doubling bifurcation, Neimark-Sacker bifurcation, and pitchfork bifurcation are introduced for the fixed point. The method for computing the bifurcation points of the equilibrium point and the periodic points is also introduced, and an example of an application is presented.

Fractional-order calculus is the branch of mathematics which deals with non-integerorder differentiation and integration. Fractional calculus has recently found its way to engineering applications; particularly electronic circuits with promising results showing the feasibility of fabricating fractional-order capacitors on silicon. Fractionalorder capacitors are lossy non-deal capacitors with an impedance given by Zc = (1/jωC)α, where C is the pseudo-capacitance and α is its order (0 < α ≤ 1). When these fractional-order capacitors are employed within an oscillator (sinusoidal or relaxation) circuit, this oscillator is called a fractional-order oscillator and is described by non-integer-order differential equations. Therefore, an oscillator of order 1.5 or 2.6 is possible to obtain. While the oscillation frequency in integer-order oscillators is related to their RC time constants, fractional-order oscillators have their oscillation frequencies also related to α. This adds more design freedom and enables extremely high or extremely low oscillation frequencies even with large RC time constants. This chapter aims at reviewing the theory of designing fractional-order oscillators accompanied by several design examples. Experimental results are also shown.

In this chapter, two astable oscillators are introduced by making use of memristor and memcapacitor emulators, respectively. First, the oscillating characteristics of an astable multivibrator based on flux-controlled memristor emulator and 555 timer are explored. Then, another astable oscillator is newly implemented based on one floating memcapacitor emulator and two NOT gates. The inclusion of memristor or memcapacitor in the astable oscillators provides a new option allowing for large degree of flexible control over frequency as well as duty ratio.

The analysis of nonlinear phenomena in continuous-time dynamics is one of important topics in the field of engineering, and it has attracted many researchers in recent years. The researchers have tried to solve this problem by simplifying the nonlinear dynamics. We introduce extremely simple oscillators whose dynamics are represented by piecewise-constant equations, and show two examples. One of them is a chaotic spiking oscillator with piecewise-constant vector field. We analytically prove the generation of chaos by using Poincaré map which is derived through a simple systematic procedure. Another is a coupled system of piecewise-constant oscillators. The parameter regions of in-phase and anti-phase synchronization are clarified by using a fast calculation algorithm. Some theoretical results are verified in the experimental circuits.

This chapter focuses on the case where the common external force of some relaxation oscillators is a nonperiodic signal. The objective relaxation oscillator is regarded as an electronic firefly (EFF) circuit. By using the implemented EFF circuits, the synchronisation phenomena induced by the common external force is observed. Firstly, a case is considered where the external force is a periodic pulse signal. Then, the case where the external force is a nonperiodic pulse signal is investigated. The paper clarifies the relationship between the individual fundamental synchronisation range and the noise synchronisation range by the implementation measurements.

This chapter investigates multimode oscillations and localized oscillation modes in inductor-coupled hard oscillators, which are considered as a form of a van der Pol oscillators with relatively higher-order nonlinearity. First, the method of averaging for weakly nonlinear oscillators is surveyed. Then, the averaged equation of the two inductor-coupled oscillators is derived. In particular, we show that a double-mode oscillation is stably excited in the coupled system for weakly nonlinear oscillators. When the nonlinearity of the coupled system becomes stronger, the double-mode oscillation disappears, whereas a localized oscillation mode emerges. Furthermore, we investigate a propagating wave phenomenon and a localized mode observed in the six inductor-coupled hard-oscillator rings. We show that the propagating wave corresponds to a multimode oscillation with several dominant peaks in a spectral distribution, and that the solution originates in the neighbourhood of a local bifurcation point of the localized mode.

There are many synchronization phenomena in coupled oscillator arrays. There is a wave of a phase difference which is one of synchronization phenomena. The wave, which a phase difference between adjacent oscillators propagates, continuously exists. We call the wave a phase-inversion wave. The phase-inversion waves can be observed on a ladder and a cross constructed by van der Pol oscillators. In this section, the phase-inversion waves are introduced.

Coupled oscillatory circuits provide simple models for describing high-dimensional nonlinear phenomena occurring in our everyday world. We often feel that the coupled oscillatory networks behave like human, especially, when we carry out circuit experiments. In this chapter, we pay our attention to frustration influence for synchronization phenomena of coupled oscillatory networks. We consider two types of coupled oscillatory networks with frustration. First one is that the oscillator in a ring-coupled van der Pol oscillator has different frequency to the others. Second one is that the coupling structure affects the synchronization state in coupled polygonal oscillatory networks.

We study bounds on the coupling strengths required to synchronize dynamical systems coupled via undirected and directed complex networks. In particular, we leverage tools from spectral graph theory to derive conditions based on the topological structures of the networks.

This chapter recalls a collection of experimental results on reconfigurable topology networks of oscillators, with Chua's circuits as chaotic dynamical nodes. Collective behaviours arising from network node interactions, such as global synchronization, emergence of clusters, patterns and waves formation, have been observed in a setup expressly developed [1-7].

Tuned power oscillators are important power-electronics circuits for achieving high power density. In addition, it is possible to apply the soft-switching techniques and high power-conversion efficiency can be achieved at high frequencies. This chapter presents fundamental operation and design of high-frequency high-efficiency tuned power oscillator. Concretely, the class-B oscillator family is introduced along with operation principle and design example.

In this chapter, we explain important role of ring oscillators in generating random bit streams in logic devices. We consider three types of ring oscillators used as sources of jittery clock signals: single-event ring oscillators, multi-event ring oscillators with collision and multi-event ring oscillator without collision, i.e. self-timed rings. We present some representative examples of oscillator-based true random number generators and their characteristics.

In this chapter, we describe a complete attack on a ring oscillator (RO) based true random number generator using the electromagnetic side channel. First, we analyze the frequency of the oscillators and their placement in the device. This analysis leads to the active attack that modifies the behavior of the random number generator using a strong electromagnetic field. We show that it is possible to dynamically control the bias of a RO based random number generator implemented in logic devices.